Question

An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is --$250 and the standard deviation of the loss is ơ-$1000. The distribution of losses is strongly right-skewed: many policies have $0 loss, but a few have large losses. An auditor examines a random sample of 10,000 of the company's policies. If the company's clairm is correct, what's the probability that the average loss from fire in the sample is no greater than $275?

Answer 1

Answer:

the probability that the average loss from fire in the sample is no greater than $275 is 0.9938

Step-by-step explanation:

given information:

mean, μ = $250

std deviation, σ = $1000

random sample, n = 10000

x = $275

P($x$ ∠_ 275) = P(z < (z ∠ (x - μ)/(σ/√n))

                    = P (z ∠ (275 - 250)/(1000/√10000)

                    = P(z ∠ 2.5)

                     =  0.9938